An Algorithm for Minimizing Roundoff Noise in Cascade Realizations of Finite Impulse Response Digital Filters

As discussed in previous works, 1 2 the implementation of F I R filters using finite precision arithmetic has become an important issue in recent years. For cascade realizations of F I R filters, roundoff noise is a crucial problem. In Refs. 1 and 2, some of the theoretical bases for the analysis of roundoff noise in the F I R cascade form have been considered. This paper presents a large body of experimental results which depict the dependence of roundoff noise on several of the important parameters of a cascade F I R low-pass filter. Most importantly, these results point to an algorithm which can find efficiently, for a cascade filter, an ordering which has a noise variance very close to the minimum possible. Experimental verification of this algorithm for a wide range of filters is presented. Low-pass, extraripple 3 filters are used throughout these investigations as being representative of F I R filters. It will be seen that most results * This paper is based on a thesis1 submitted in partial fulfillment of the requirements for the degrees of Bachelor of Science and Master of Science in the Department of Electrical Engineering at the Massachusetts Institute of Technology in September 1972. 347